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Unformatted text preview: 1 1 Chapter 7 Atmospheric Transmission 2 Beer-Lambert-Bouguer Law: F = F exp (kx) Bouguer-Lambert Law: Change in irradiance is proportional to path length and incident irradiance k is the absorption coefficient : units = cm-1 ( a in Petty) k (B&amp;C) = a (Petty) = 4 n i / Beer realized that k is proportional to the concentration of absorbers: k = a N N is the molecular number density (cm-3 ) NOT TO BE CONFUSED WITH REFRACTIVE INDEX N !!! a ( ) is the absorption cross section : units = cm 2 ( effective area of molecule) So the Beer-Lambert-Bouguer Law often called Beers Law states that radiation incident on an absorbing medium is attenuated exponentially at a rate that is determined by the incident intensity, path length, concentration of absorbers, and absorption cross section. The cross section is determined by the molecular characteristics. Review Chapter 7. Atmospheric Transmission 2 3 Using Petty Notation: ( ) ( ) x I x I a = exp , Interpretation : Intensity (radiance) drops off exponentially with distance (x) as radiation propagates through homogeneous absorbing medium with absorption coefficient a cm-1 . How else is radiation attenuated? Attenuation can also occur via scattering: redirection of radiation from original propagation direction via interaction with matter. (Do not yet consider scattering into the direction of propagation) s a e + = e is extinction coefficient; a is absorption coefficient; s is scattering coefficient Analogous to a , s = s N, where s is the scattering cross-section (cm 2 ) and N is the number density of the scatterer (cm-3 ). We introduce the single scattering albedo to characterize the relative importance of absorption and scattering in any medium: a s s e s + = = ~ Note: all quantities are wavelength dependent! 4 Recall the differential form of Beers Law: Integrate from s1 to s2: ds I dI e = = 2 1 2 1 ) ( 1 s s e s s ds s dI I ( ) ( ) ( ) = 2 1 1 2 exp s s e ds s s I s I This can be written as: ( ) [ ] = = s2 s1 e 2 1 2 1 ) , ( where , exp ) , ( ds s s s s s t Here t (s 1 ,s 2 ) is the transmission over the path from s 1 to s 2 . t = [ I(s 2 ) / I(s 1 ) ]. (dimensionless) is the optical path or optical depth or optical thickness . By convention, optical depth refers to extinction in the vertical direction. The terms optical depth and optical thickness are often used interchangeably, but occasionally optical thickness refers to extinction through the entire depth of the atmosphere, whereas optical depth refers to extinction through just a fraction of the atmosphere....
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- Fall '10